We use linear stability analysis to approximate the axisymmetric to nonaxisymmetric transition in the differentially heated rotating annulus. We study an accurate mathematical model that uses the Navier– Stokes equations in the Boussinesq approximation. The steady axisymmetric solution satisfies a two-dimensional partial differential boundary value problem. It is not possible to compute the sol...

An analysis is presented of parametric instability in a finite-length rotating cylinder subject to periodic axial compression by small sinusoidal oscillations of one of its ends (the ‘piston’). The instability is due to resonant interactions between inertialwave (Kelvin) modes of the cylinder and the oscillatory compression and is resisted by viscosity, acting both through thin boundary layers ...

This paper presents a quasi-local method of studying the physics of dynamical black holes in numerical simulations. This is done within the dynamical horizon framework, which extends the earlier work on isolated horizons to time-dependent situations. In particular: (i) We locate various kinds of marginal surfaces and study their time evolution. An important ingredient is the calculation of the ...

Global stationary configurations of both aligned and logarithmic spiral magnetohydrodynamic (MHD) perturbations are constructed analytically within an axisymmetric background of razor-thin scale-free gas disc, which is embedded in an axisymmetric gravitational potential of a dark matter halo and involves an isopedic magnetic field almost vertically threaded through the disc plane. The scale-fre...

In this paper, the axisymmetric and non-axisymmetric buckling of finite elastic cylindrical shell, which is impacted on the end by axial step loads, is discussed with the aid of the stress wave propagating and reflecting. By solving the disturbed equations, the bifurcation condition of the dynamic buckling, critical buckling load and buckling mode are obtained. The results show that when the th...

We extend our previous immersed boundary (IB) method for 3D axisymmetric inextensible vesicle in Navier-Stokes flows, [W.-F. Hu, Y. Kim, M.-C. Lai, An immersed boundary method for simulating the dynamics of three-dimensional axisymmetric vesicles in Navier-Stokes flows, J. Comput. Phys. 257 (2014)] to general three dimensions. Despite a similar spirit in numerical algorithms to the axisymmetric...

We develop in this paper a numerical method to simulate three-dimensional incompressible flows based on a decomposition of the flow into an axisymmetric part, in terms of the stream function and the circulation, and a non-axisymmetric part in terms of a potential vector function. The method is specially suited for the study of nonlinear stability of axially symmetric flows because one may follo...

We develop variational principles to study the structure and the stability of equilibrium states of axisymmetric flows. We show that the axisymmetric Euler equations for inviscid flows admit an infinite number of steady state solutions. We find their general form and provide analytical solutions in some special cases. The system can be trapped in one of these steady states as a result of an inv...

Thermodynamics of vorticity density fields ~v/r! in axisymmetric flows are considered, and the statistical equilibrium theories of Miller, Weichman, and Cross @Phys. Rev. A 45, 2328 ~1992!#, Robert and Sommeria @J. Fluid Mech. 229, 291 ~1991!#, and Turkington @Comm. Pure Appl. Math. 52, 781 ~1999!# for the two-dimensional flows in Cartesian coordinates are extended to axisymmetric flows. It is ...